A Study of MAP Estimation Techniques for Nonlinear Filtering
Paper in proceedings, 2012
For solving the nonlinear filtering problem, much
attention has been paid to filters based on the Linear Minimum Mean Square Error (LMMSE) estimation. Accordingly, less attention has been paid to MAP estimation techniques in this field. We argue that, given the superior performance of the latter in certain situations, they deserve to be more carefully investigated. In this paper, we look at MAP estimation from optimization perspective. We present a new method that uses this technique for solving the nonlinear filtering problem and we take a look at two existing methods. Furthermore, we derive a new method to reduce the dimensionality of the optimization problem which helps decreasing the computational complexity of the algorithms. The performance of MAP estimation techniques
is analyzed and compared to LMMSE filters. The results show
that in the case of informative measurements, MAP estimation
techniques have much better performance.